Comparison results on the preconditioned mixed-type splitting iterative method for M-matrix linear systems

Document Type : Research Paper

Authors

1 Shahid Bahonar University of Kerman

2 Vali-Asr University of Rafsanjan

Abstract

Consider the linear system Ax=b where the coefficient
matrix A is an M-matrix. In the present work, it is proved
that the rate of convergence of the Gauss-Seidel method is faster
than the mixed-type splitting and AOR (SOR) iterative methods for
solving M-matrix linear systems. Furthermore, we improve the rate
of convergence of the mixed-type splitting iterative method by
applying a preconditioned matrix. Comparison theorems show that
the rate of convergence of the preconditioned Gauss-Seidel method
is faster than the preconditioned mixed-type splitting and AOR
(SOR) iterative methods. Finally, some numerical examples are
presented to illustrate the reality of our comparison theorems.

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History

  • Receive Date: 03 September 2010
  • Revise Date: 04 December 2010
  • Accept Date: 04 December 2010
  • First Publish Date: 15 July 2012

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